The mammals are the class of vertebrateanimals primarily characterized by the presence of mammary glands in the female which produce milk for the nourishment of young; the presence of hair or fur; and which have endothermic or "warm blooded" bodies.
The brain regulates endothermic and circulatory systems, including a four-chambered heart. Mammals embrace more than 5,000 genera, distributed in 425 families and up to 46 orderss (the number depends on the classification scheme adopted).

While monotremes do not have nipples, they do have mammary glands, meaning that they meet all conditions for inclusion in the class Mammalia. It should be noted that the current trend in taxonomy is to emphasize common ancestry; the diagnostic characteristics are useful for identifying this ancestry, but if, for example, a cetacean were found that had no hair at all, it would still be classed as a mammal.

Mammals have three bones in each ear and one (the dentary) on each side of the lower jaw; all other vertebrates with ears have one bone (the stapes) in the ear and at least three on each side of the jaw. A group of therapsids called cynodonts had three bones in the jaw, but the main jaw joint was the dentary and the other bones conducted sound.

The epidermis is typically ten to thirty cells thick, its main function being to provide a waterproof layer. Its outermost cells are constantly lost; its bottommost cells are constantly dividing and pushing upward. The middle layer, the dermis, is fifteen to forty times thicker than the epidermis. The dermis is made up of many components such as bony structures and blood vessels. The hypodermis is made up of adipose tissue. Its job is to store lipids, and to provide cushioning and insulation. The thickness of this layer varies widely from species to species.

Mammals belong among the amniotes, and in particular to a group called the synapsids, distinguished by the shape of their skulls. Within this group they developed from the therapsidss, and more specifically the eucynodonts, 220 million years ago during the Triassic period. During the Mesozoic period they diversified into the three main groups found today (monotremes, marsupials, and placentals). They remained small and shrew-like throughout the era, but rapidly developed into larger forms following the Cretaceous-Tertiary extinction event 65 million years ago.

George Gaylord Simpson's classic Principles of Classification and a Classification of Mammals (AMNH Bulletin v. 85, 1945) was the original source for the taxonomy listed here. Simpson laid out a systematics of mammal origins and relationships that was universally taught until the end of the 20th Century. Since Simpson's 1945 classification, the paleontological record has been recalibrated, and the intervening years have seen much debate and progress concerning the theoretical underpinnings of systematization itself, partly through the new concept of cladistics (q.v.). Though field work gradually made Simpson's classification outdated, it remained the closest thing to an official classification of mammals.

In 1997, the mammals were comprehensively revised by Malcolm C. McKenna and Susan K. Bell, which has resulted in the McKenna/Bell classification.

McKenna and Bell, Classification of Mammals: Above the species level, (1997) is the most comprehensive work to date on the systematics, relationships, and occurrences of all mammal taxa, living and extinct, down through the rank of genus. The new McKenna/Bell classification was quickly accepted by paleontologists. The authors work together as paleontologists at the American Museum of Natural History, New York. McKenna inherited the project from Simpson and, with Bell, constructed a completely updated hierarchical system, covering living and extict taxa that reflects the historical genealogy of Mammalia.

The McKenna/Bell hierarchical listing of all of the terms used for mammal groups above the species includes extinct mammals as well as modern groups, and introduces some fine distinctions such as legions and sublegions (categories which fall between classes and orders) that are likely to be glossed over by the layman.

The published re-classification forms both a comprehensive and authoritative record of approved names and classifications and a list of invalid names.